The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 have in common.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

2,070,000 in scientific notation is 2.07 x 10⁶

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 27 - 15 = 12 new staff for the busy season.

Diane scored 78% on the test meaning she earned 78% of the possible points on the test. There were 300 possible points on the test so she earned 300 x 0.78 = 234 points. Each question is worth 3 points so she got \( \frac{234}{3} \) = 78 questions right.

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{10 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 4